Question

(sinq, cosq) and (3, 2) lie on the same side of the line

x + y = 1, then q lies between-

• A. $\left( 0,\frac{\pi}{2} \right)$
• B. (0, p)
• C. $\left( \frac{\pi}{4},\frac{\pi}{2} \right)$
• D. $\left( 0,\frac{\pi}{4} \right)$

Answer 1

Answer: (D)

$\left( 0,\frac{\pi}{4} \right)$

Answer 2

(sinq, cosq) & (3, 2) lie on the same side of the line
x + y – 1 = 0 Ž (sinq + cosq – 1) (3 + 2 – 1) > 0

4 (sinq + cosq – 1) > 0 Ž sinq + cosq > 1

$\frac{1}{\sqrt{2}}$sinq + $\frac{1}{\sqrt{2}}$cosq >$\frac{1}{\sqrt{2}}$Ž sin(q + p/4) > $\frac{1}{\sqrt{2}}$

$\frac{\pi}{4}$ < q + $\frac{\pi}{4}$ < $\frac{\pi}{2}$Ž 0 < q < p/4 Ž q Ī (0, p/4)